1. Researchers developed a safety performance function (SPF), which estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments ofroadway, they fit the model E(y)=β0+β1x1+β2x2, where y=number of crashes per three years, x1=roadway length (miles), and x2=average annual daily traffic (number of vehicles) equals=AADT.

Table of the Model Result

Interstate Highways

Variable	Parameter Estimate	Standard Error	t-value
Intercept	1.87027	0.54371	3.93
Length (x1)	0.14977	0.02456	4.59
AADT (x2)	0.00018	0.00003	5.46

Variable

Parameter Estimate Standard Error t-value Intercept

1. 21104 0.32226 4.57842

Length (x1) 0.63524 0.01299 3.28315

AADT (x2) 0.00046 0.00015 4.23762

a. Give the least squares prediction equation for the interstate highway model.

y= (.....) + (.....) x1 + ..... x2

b. Give practical interpretations of the β estimates you made in part

a. Interpret the value of β0. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

B. This value has no meaningful interpretation because x1=0 and 0x2=0 are not in the observed range.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

Interpret the value of β1. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

C. This value has no meaningful interpretation because 0 x1=0 and x2=0 are not in the observed range.

Interpret the value of β2. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

B. This value has no meaningful interpretation because 0 x1=0 and 0x2=0 are not in the observed range.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

c. Refer to part a. Find a 99% confidence interval for β1.

(....), (....) (Round to five decimal places as needed.)

Interpret the result. Choose the correct answer below.

A. There is not enough information to answer this question.

B. We are 9% confident that the increase in mean number of crashes for each additional mile of roadway is between left limit and right limit, holding AADT constant.

C. We are 1% confident that the increase in mean number of crashes for each additional mile of roadway is between left limit and right limit, holding AADT constant.

d. Refer to part a. Find a 99% confidence interval for β2.

(....), (....) (Round to five decimal places as needed.)

Interpret the result. Choose the correct answer below.

A. We are 99% confident that the increase in mean number of crashes for each additional vehicle per day is between left limit and right limit, holding roadway mileage constant.

B. There is not enough information to answer this question.

C. We are 1% confident that the increase in mean number of crashes for each additional vehicle per day is between left limit and right limit, holding roadway mileage constant.

e. Give the least squares prediction equation for the interstate non-highway model.

y=..... + ..... x 1 + .... x2

Give practical interpretations of the β estimates you made in previous part. Interpret the value of β0. Choose the correct answer below.

A. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

Interpret the value of β1. Choose the correct answer below.

A. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

Interpret the value of β2. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per day, holding roadway mileage constant.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant.

C. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

Find a 99% confidence interval for β1.

(.... , .....) (Round to five decimal places as needed.)

Find a 99% confidence interval for β2.

(.... , .... ) (Round to five decimal places as needed.)